We investigate the conditions under which the symmetric functions are Schur -power convex for and . As a consequence, we prove that these functions are Schur geometrically convex and Schur harmonically convex, which generalizes some known results. By applying the theory of majorization, several inequalities involving the th power mean and the arithmetic, the geometric, or the harmonic means are presented.
"Schur -Power Convexity of a Class of Multiplicatively Convex Functions and Applications." Abstr. Appl. Anal. 2014 1 - 12, 2014. https://doi.org/10.1155/2014/258108